THE NATURE AND EXTENT OF KNOWLEDGE.
The third book of Locke's Essay is upon words and language; and in the
order of treatment this would be the next topic for discussion. But
much of what is said in this connection both by Locke and by Leibniz is
philological, rhetorical, and grammatical in character, and although
not without interest in itself, is yet without any especial bearing
upon the philosophical points in controversy. The only topics in
this book demanding our attention are general and particular terms;
but these fall most naturally into the discussion of general and
particular knowledge. In fact, it is not the terms which Locke
actually discusses, but the ideas for which the terms stand. We
pass on accordingly, without further ceremony, to the fourth book,
which is concerning knowledge in general. Locke defines knowledge
as "nothing but the perception of the connection and agreement, or
disagreement and repugnancy, of any of our ideas." These agreements or
disagreements may be reduced to four sorts,--Identity, or diversity;
Relation; Co-existence, or necessary connection; Real existence. The
statement of identity and diversity is implied in all knowledge
whatsoever. By them "the mind clearly and infallibly perceives each
idea to agree with itself and be what it is, and all distinct ideas to
disagree; _i. e._, the one not to be the other." The agreement of
relation is such knowledge as the mind derives from the _comparison_
of its ideas. It includes mathematical knowledge. The connection of
co-existence "belongs particularly to substances." Locke's example
is that "gold is fixed,"--by which we understand that the idea of
fixedness goes along with that group of ideas which we call gold. All
statements of fact coming under the natural sciences would fall into
this class. The fourth sort is "that of actual and real existence
agreeing to any idea."
Leibniz's criticism upon these statements of Locke is brief and to
the point. He admits Locke's definition of knowledge, qualifying it,
however, by the statement that in much of our knowledge, perhaps in all
that is merely empirical, we do not know the reason and connection
of things and hence cannot be said to _perceive_ the agreement
or disagreement of ideas, but only to feel it confusedly. His
most important remark, however, is to the effect that relation is
not a special kind of knowledge, but that all Locke's four kinds
are varieties of relation. Locke's "connection" of ideas which
makes knowledge is nothing but relation. And there are two kinds of
relation,--those of "comparison" and of "concourse." That of comparison
states the identity or distinction of ideas, either in whole or in
part. That of concourse contains Locke's two classes of co-existence
and existence. "When we say that a thing really exists, this existence
is the predicate,--that is to say, a notion connected with the idea
which is the subject; and there is connection between these two
notions. The existence of an object of an idea may be considered as
the concourse of this object with me. Hence comparison, which marks
identity or diversity, and concourse of an object with me (or with the
_ego_) are the only forms of knowledge."
Leibniz leaves the matter here; but he only needed to develop what is
contained in this statement to anticipate Berkeley and Kant in some of
the most important of their discoveries. The contradiction which lies
concealed in Locke's account is between his definition of knowledge
in general, and knowledge of real existence in particular. One is the
agreement or disagreement of _ideas_; the other is the agreement of
an idea _with an object_. Berkeley's work, in its simplest form, was
to remove this inconsistency. He saw clearly that the "object" was an
intruder here. If knowledge lies in the connection of _ideas_, it is
impossible to get outside the ideas to find an object with which they
agree. Either that object is entirely unknown, or it is an idea. It
is impossible, therefore, to find the knowledge of reality in the
comparison of an idea with an object. It must be in some property of
the ideas themselves.
Kant developed more fully the nature of this property, which
constitutes the "objectivity" of our ideas. It is their connection
with one another according to certain _necessary_ forms of perception
and rules of conception. In other words, the reality of ideas lies in
their being connected by the necessary and hence universal relations
of synthetic intelligence, or, as Kant often states it, in their
agreement with the conditions of self-consciousness. It is not, I
believe, unduly stretching either the letter or the spirit of Leibniz
to find in that "concourse of the object with the ego" which makes
its reality, the analogue of this doctrine of Kant; it is at all
events the recognition of the fact that reality is not to be found
in the relating of ideas to unknown things, but in their relation to
self-conscious intelligence. The points of similarity between Kant
and Leibniz do not end here. Leibniz's two relations of "comparison"
and "concourse" are certainly the congeners of Kant's "analytic"
and "synthetic" judgments. But Leibniz, as we shall see hereafter,
trusts too thoroughly to the merely formal relations of identity and
contradiction to permit him such a development of these two kinds of
relation as renders Kant's treatment of them epoch-making.
The discussion then advances to the subject of degrees of knowledge,
of which Locke recognizes three,--intuitive, demonstrative, and
sensitive. Intuitive knowledge is immediate knowledge,--recognition
of likeness or difference without the intervention of a third idea;
it is the most certain and clear of all knowledge. In demonstrative
knowledge the agreement or disagreement cannot be perceived directly,
because the ideas cannot be put together so as to show it. Hence
the mind has recourse to intermediaries. "And this is what we call
reasoning." Demonstrative rests on intuitive knowledge, because each
intermediate idea used must be immediately perceived to be like or
unlike its neighboring idea, or it would itself need intermediates for
its proof. Besides these two degrees of knowledge there is "another
perception of the mind employed about the particular existence of
finite things without us, which, going beyond bare probability, and yet
not reaching perfectly to either of the foregoing degrees of certainty,
passes under the name of knowledge."
Leibniz's comments are again brief. The primitive truths which are
known by intuition are to be divided into two classes,--truths of
reason and of fact. The primitive truths of reason are necessary, and
may be called identical, because they seem only to repeat the same
thing, without teaching us anything. A is A. A is not non-A. Such
propositions are not frivolous or useless, because the conclusions
of logic are demonstrated by means of identical propositions, and
many of those of geometry by the principle of contradiction. All the
intuitive truths of reason may be said to be made known through the
"immediation" of ideas. The intuitive truths of fact, on the other
hand, are contingent and are made known through the "immediation"
of feeling. In this latter class come such truths as the Cartesian,
"I think, therefore I am." Neither class can be proved by anything more
certain.
Demonstration is defined by Leibniz as by Locke. The former recognizes,
however, two sorts,--analytic and synthetic. Synthesis goes from the
simple to the complex. There are many cases, however, where this is
not applicable; where it would be a task "equal to drinking up the sea
to attempt to make all the necessary combinations. Here the method
of exclusions should be employed, cutting off many of the useless
combinations." If this cannot be done, then it is analysis which gives
the clew into the labyrinth. He is also of the opinion that besides
demonstration, giving certainty, there should be admitted an art of
calculating probabilities,--the lack of which is, he says, a great
defect in our present logic, and which would be more useful than a
large part of our demonstrative sciences. As to sensitive knowledge,
he agrees with Locke that there is such a thing as real knowledge
of objects without us, and that this variety does not have the same
metaphysical certainty as the other two; but he disagrees regarding
its criterion. According to Locke, the criterion is simply the greater
degree of vividness and force that sensations have as compared with
imaginations, and the actual pleasures or pains which accompany
them. Leibniz points out that this criterion, which in reality is
purely emotional, is of no great value, and states the principle of the
reality of sensible phenomena which we have already given, repeating
that it is found in the _connection_ of phenomena, and that "this
connection is verified by means of the truths of reason, just as the
phenomena of optics are explained by geometry."
The discussion regarding "primitive truths," axioms, and maxims,
as well as the distinction between truths of fact and of reason, has
its most important bearing in Locke's next chapter. This chapter has
for its title the "Extent of Human Knowledge," and in connection with
the sixth chapter, upon universal propositions, and with the seventh,
upon axioms, really contains the gist of the treatment of knowledge. It
is here also that are to be considered chapters three and six of book
third, having respectively as their titles, "Of General Terms," and "Of
the Names of Substances."
To understand Locke's views upon the extent and limitations of our
knowledge, it is necessary to recur to his theory of its origin. If
we compare what he says about the origin of ideas from sensations
with what he says about the development of general knowledge from
particular, we shall find that Locke unconsciously puts side by side
two different, and even contradictory, theories upon this point. In the
view already given when treating of sensation, knowledge originates
from the combination, the addition, of the simple ideas furnished
us by our senses. It begins with the simple, the unrelated, and
advances to the complex. But according to the doctrine which he
propounds in treating of general terms, knowledge begins with the
individual, which is already qualified by definite relations, and
hence complex, and proceeds, by abstracting some of these qualities,
towards the simple. Or, in Locke's own language, "ideas become general
by separating from them the circumstances of time and place and any
other ideas that may _determine_ them to this and that particular
existence." And, still more definitely, he says that general ideas
are framed by "leaving out of the _complex_ idea of individuals that
which is peculiar to each, and retaining only what is common to them
all." From this it follows that "general and universal belong not to
the real existence of things, but are the inventions and creatures of
the understanding." "When we quit particulars, the generals that rest
are only creatures of our own making. . . . The signification
they have is nothing but a relation that by the mind of man is added
to them." And in language which reminds us of Kant, but with very
different bearing, he says that relations are the workmanship of the
understanding. The abstract idea of what is common to all the members
of the class constitutes "nominal essence." This nominal essence, not
being a particular existence in nature, but the "workmanship of the
understanding," is to be carefully distinguished from the real essence,
"which is the being of anything whereby it is what it is." This real
essence is evidently equivalent to the unknown "substance" of which we
have heard before. "It is the real, internal, and unknown constitution
of things." In simple or unrelated ideas and in modes the real and
the nominal essence is the same; and hence whatever is demonstrated of
one is demonstrated of the other. But as to substance it is different,
the one being natural, the other artificial. The nominal essence always
relates to sorts, or classes, and is a pattern or standard by which we
classify objects. In the individual there is nothing essential, in this
sense. "Particular beings, considered barely in themselves, will be
found to have all their qualities equally essential to them, or, which
is more, nothing at all." As for the "real essence" which things have,
"we only suppose its being without precisely knowing what it is."
Locke here presents us with the confusion which, in one form or
another, is always found in empiricism, and which indeed is essential
to it. Locke, like the ordinary empiricist, has no doubt of the
existence of real things. His starting-point is the existence of two
substances, mind and matter; while, further, there is a great number of
substances of each kind. Each mind and every separate portion of matter
is a distinct substance. This supposed deliverance of common sense
Locke never called into question. Working on this line, all knowledge
will consist in abstraction from the ready-made things presented to us
in perception, "in leaving out from the complex idea of individuals"
something belonging to them. But on the other hand, Locke never doubts
that knowledge begins with sensation, and that, therefore, the process
of knowledge is one of adding simple, unrelated elements. The two
theories are absolutely opposed to each other, and yet one and the
same philosophical inference may be drawn from each; namely, that only
the particular is real, and that the universal (or relations) is an
artificial product, manufactured in one case by abstraction from the
real individual, in the other by compounding the real sensation.
The result is, that when he comes to a discussion of the extent of
knowledge, he admits knowledge of self, of God, and of "things,"
only by a denial of his very definition of knowledge, while knowledge
of other conceptions, like those of mathematics, is not knowledge of
reality, but only of ideas which we ourselves frame. All knowledge,
that is to say, is obtained only either by contradicting his own
fundamental notion, or by placing it in relations which are confessedly
artificial and superinduced. It is to this point that we come.
The proposition which is fundamental to the discussion is that we
have knowledge only where we perceive the agreement or disagreement
of ideas. Locke then takes up each of his four classes of connection,
in order to ascertain the extent of knowledge in it. Our knowledge
of "identity and diversity extends as far as our ideas," because we
intuitively perceive every idea to be "what it is, and different from
any other." Locke afterwards states, however, that all purely identical
propositions are "trifling," that is, they contain no instruction;
they teach us nothing. Thus the first class of relations cannot be
said to be of much avail. If we consider the fourth kind of knowledge,
that of real existence, we have an intuitive knowledge of self, a
demonstrative knowledge of God, and a sensitive knowledge of other
things. But sensitive knowledge, it must be noted, "does not extend
beyond the objects _actually present_ to our senses." It can hardly
be said, therefore, to assure us of the existence of _objects_
at all. It only tells us what experiences are being at the time
undergone. Furthermore, knowledge of all three (God, self, and matter),
since of real being, and not of relations between ideas, contradicts
his definition of knowledge. But perhaps we shall find knowledge more
extended in the other classes. And indeed Locke tells us that knowledge
of relations is the "largest field of our knowledge." It includes
morals and mathematics; but it is to be noticed that, according to
Locke, in both of these branches our demonstrations are not regarding
facts, but regarding either "modes" framed by ourselves, or relations
that are the creatures of our minds,--"extraneous and superinduced"
upon the facts, as he says. He thus anticipates in substance, though
not in phraseology, Hume's distinction between "matters of fact" and
"connections of ideas," in the latter of which we may have knowledge,
but not going beyond the combinations that we ourselves make.
This leaves one class, that of co-existence, to be examined. Here,
if anywhere, must knowledge, worthy of being termed scientific, be
found. This class, it will be remembered, comprehends our knowledge
concerning substances. But this extends, according to Locke, "a
very little way." The idea of a substance is a complex of various
"simple ideas united in one subject and co-existing together." When we
would know anything further concerning a substance, we only inquire
what other simple ideas, besides those already united, co-exist with
them. Since there is no _necessary_ connection, however, among these
simple ideas, since each is, by its very simplicity, essentially
distinct from every other, or, as we have already learned, since
nothing is essential to an individual, we can never be sure that any
idea really co-exists with others. Or, as Locke says, in physical
matters we "can go no further than particular experience informs us
of. . . . We can have no certain knowledge of universal truths
concerning natural bodies." And again, "universal propositions of whose
truth and falsehood we have certain knowledge concern not existence;"
while, on the other hand, "particular affirmations are only concerning
existence, declaring only the _accidental_ union or separation of ideas
in things existing." This particular knowledge, it must be recalled,
is, in turn, only sensitive, and thus extends not beyond the time when
the sensation is had.
We are not surprised then at learning from Locke that regarding bodies
"we are not capable of scientific knowledge." "Natural philosophy is
not capable of being made a science;" or, as Locke elsewhere states it,
knowledge regarding the nominal essence is "trifling" (Kant's analytic
judgment); regarding the real essence is impossible. For example,
when we say that all gold is fusible, this means either simply that
fusibility is one of the ideas which we combine to get the general
idea of gold, so that in making the given judgment we only expand
our own notion; or it means that the "real" substance gold is always
fusible. But this is a statement we have no right to make, and for two
reasons: we do not know what the real substance gold is; and even if we
did, we should not know that fusibility _always_ co-exists with it. The
summary of the whole matter is that "general certainty is to be found
only in our ideas. Whenever we go to seek it elsewhere, in experiment
or observations without us, our knowledge goes not beyond particulars."
It has been necessary to give an account of Locke's views at this
length because it is in his discussion of the limitations and extent
of knowledge that his theory culminates. While not working out his
sensationalism as consistently as did Hume, he yet reduces knowledge
to that of the existence of God and ourselves (whose natures, however,
are unknown), and to a knowledge of mathematical and moral relations,
which, however, concerns only "the habitudes and relations of abstract
ideas." We have now to see by what means Leibniz finds a wider sphere
for certain and general knowledge by his theory of intellectualism than
Locke can by his sensationalism.
Leibniz's theory of knowledge rests upon a distinction between truths
of fact, which are _a posteriori_ and contingent, and truths of
reason, which are _a priori_ and necessary. In discussing his views
regarding experience, we learned that, according to him, all judgments
which are empirical are also particular, not allowing any inference
beyond the given cases experienced. Experience gives only instances,
not principles. If we postpone for the present the discussions of
truths of reason, by admitting that they may properly be said to be
at once certain and universal, the question arises how in matters
of fact there can be any knowledge beyond that which Locke admits;
and the answer is, that so far as the mere existence and occurrence
of these facts is concerned, there is neither demonstrative nor
general knowledge. But the intelligence of man does not stop with the
isolated fact; it proceeds to inquire into its cause, to ascertain
its conditions, and thus to see into, not merely its actual existence,
but its _possibility_. In Leibniz's language: "The real existence of
things that are not necessary is a point of fact or history; but the
knowledge of possibilities or necessities (the necessary being that
whose opposite is not possible) constitutes demonstrative science." In
other words, it is the principle of causality, which makes us see a
fact not as a mere fact, but as a dependent consequence; which elevates
knowledge, otherwise contingent and particular, into the realm of the
universal and apodictic. Underlying all "accidental union" is the real
synthesis of causation.
If we follow the discussion as it centres about the terms "nominal"
and "real," it stands as follows: Leibniz objects to the use of the
term "essence" in this connection, but is willing to accept that of
"definition;" for, as he says, a substance can have but one essence,
while there may be several definitions, which, however, all express
the same essence. The essence is the _possibility_ of that which is
under consideration; the definition is the statement of that which is
supposed to be possible. The "nominal" definition, however, while it
implies this possibility, does not expressly affirm it,--that is to
say, it may always be doubted whether the nominal definition has any
possibility (or reality) corresponding to it until experience comes
to our aid and makes us know it _a posteriori_. A "real" definition,
on the other hand, makes us know _a priori_ the reality of the thing
defined by showing us the mode of its production, "by exhibiting its
cause or generation." Even our knowledge of facts of experience cannot
be said, therefore, to be arbitrary, for we do not combine ideas just
as we please, but "our combinations may be justified by reason which
shows them to be possible, or by experience which shows them to be
actual, and consequently also possible." To take Locke's example about
gold, "the essence of gold is that which constitutes it and gives it
its sensible qualities, and these qualities, so far as they enable
us to recognize it, constitute its nominal essence, while a real
and causal definition would enable us to explain the contexture or
internal disposition. The nominal definition, however, is also real in
one sense,--not in itself, indeed, since it does not enable us to know
_a priori_ the possibility or production of the body, but empirically
real."
It is evident from these quotations that what Leibniz understands
by "possibility" is the condition or cause of a given fact; and
that, while Locke distinguishes between particular, accidental and
demonstrative, general knowledge as two opposed kinds, concerned with
two distinct and mutually exclusive spheres, with Leibniz they are
distinctions in the aspect of the same sphere of fact. In reality there
is no combination of qualities accidental, as Locke thought that by
far the greater part were; in every empirical fact there is a cause or
condition involved that is invariable, and that constitutes the reason
of the fact. The "accidental" is only in the relation of our ideas
to objects, not in the objects themselves. There may be accidental
mental associations; there are no accidental relations. In empirical,
or _a posteriori_, knowledge, so-called, the reason is there, but
is not known. _A priori_ knowledge, the real definition, discovers
and explicitly states this reason. Contingent knowledge is therefore
potentially rational; demonstrative knowledge is the actual development
of the reasons implicitly contained in experience.
We may with advantage connect this discussion with the fundamental
doctrine of Locke and Leibniz regarding intelligence and reality. To
Locke, as we have seen, knowledge is essentially a matter of relations
or connections; but relations are "superinduced" and "extraneous" as
regards the facts. Every act of knowledge constitutes, therefore, in
some way a departure from the reality to be known. Knowledge and fact
are, by their very definition, opposed to one another. But in Leibniz's
view intelligence, or reason, enters into the constitution of reality;
indeed, it is reality. The relations which are the "creatures of the
understanding" are, therefore, not foreign to the material to be known,
but are organic to it, forming its content. The process, then, in which
the mind perceives the connections or relations of ideas or objects,
is simply the process by which the mind comes to the consciousness
of the real nature of these objects, not a process of "superinducing"
unreal ideas upon them. The difficulty of Locke is the difficulty of
every theory of knowledge that does not admit an organic unity of the
knowing mind and the known universe. The theory is obliged to admit
that all knowledge is in the form of relations which have their source
in intelligence. But being tied to the view that reality is distinct
from intelligence, it is obliged to draw the conclusion that these
relations are not to be found in actual existence, and hence that all
knowledge, whatever else it may be, is unreal in the sense that it does
not and cannot conform to actual fact. But, in the theory of Leibniz,
the process of relating which is the essence of knowledge is only the
realization on the part of the individual mind of the relations or
reasons that eternally constitute reality. Since reality is, and is
what it is, through intelligence, whatever relations intelligence
rightly perceives are not "extraneous" to reality, but are its
"essence." As Leibniz says, "Truth consists in the relations between
the objects of our ideas. This does not depend upon language, but is
common to us with God, so that when God manifests a truth to us, _we
acquire what is already in his understanding_. For although there is an
infinite difference between his ideas and ours as to their perfection
and extent, yet it is always true that as to the same relation they are
identical. And it is in this relation that truth exists." To this may
be added another statement, which throws still further light on this
point: "Ideas are eternally in God, and are in us before we perceive
them."
We have now to consider somewhat more in detail the means by
which the transformation of empirical into rational knowledge
is carried on. Leibniz points out that the difficulty concerning
scientific knowledge of sensible facts is not lack of data, but,
in a certain sense, superfluity of data. It is not that we perceive
no connections among objects, but that we perceive many which we
cannot reduce to one another. "Our experiences," says Leibniz,
"are simple only in appearance, for they are always accompanied by
circumstances connected with them, although these relations are not
understood by us. These circumstances furnish material capable of
explanation and analysis. There is thus a sort of _pleonasm_ in our
perceptions of sensible objects and qualities, since we have more
than one idea of the same object. Gold can be nominally defined in
many ways. Such definitions are only _provisional_." This is to say,
empirical knowledge will become rational when it is possible to view
any subject-matter as a unity, instead of a multiplicity of varied
aspects. And on this same subject he says, in another connection: "A
great number of experiences can furnish us data more than sufficient
for scientific knowledge, provided only we have the art of using these
data." The aim of science is therefore, to discover the dynamic unity
which makes a whole of what appears to be a mere mass of accidentally
connected circumstances. This unity of relations is the individual.
It is thus evident that to Leibniz the individual is not the
beginning of knowledge, but its goal. The individual is the organic,
the dynamic unity of the variety of phases or notions presented
us in sense-experience. Individuality is not "simplicity" in
the sense of Locke; that is, separation from all relations. It
is complete connection of all relations. "It is impossible for
us to have [complete] knowledge of individuals, and to find the
means of determining exactly the individuality of anything; for
in individuality all circumstances are combined. Individuality
envelops the infinite. Only so far as we know the infinite do we
know the individual, on account of the influence (if this word be
correctly understood) that all things in the universe exercise upon
one another." Leibniz, in short, remains true to his conception of the
monad as the ultimate reality; for the monad, though an individual,
yet has the universe as its content. We shall be able, therefore, to
render our sensible experiences rational just in the degree in which we
can discover the underlying relations and dependencies which make them
members of one individual.
For the process of transformation Leibniz relies especially upon two
methods,--those of mathematics and of classification. Of the former
he here says but little; but the entire progress of physical science
since the time of Leibniz has been the justification of that little. In
the passage already quoted regarding the need of method for using our
sensible data, he goes on to say that the "infinitesimal analysis has
given us the means of allying physics and geometry, and that dynamics
has furnished us with the key to the general laws of nature." It is
certainly competent testimony to the truth of Leibniz's fundamental
principles that he foresaw also the course which the development
of biological science would take. No classification based upon
resemblances, says Leibniz in effect, can be regarded as wholly
arbitrary, since resemblances are found in nature also. The only
question is whether our classification is based upon superficial or
fundamental identities; the superficial resemblances being such as are
external, or the effects of some common cause, while the fundamental
resemblances are such as are the cause of whatever other similarities
are found. "It can be said that whatever we compare or distinguish with
truth, nature differentiates, or makes agree, also; but that nature has
differences and identities which are better than ours, which we do not
know. . . . _The more we discover the generation of species_,
and the more we follow in our classifications the conditions that
are required for their production, the nearer we approach the natural
order." Our classifications, then, so far as they depend upon what is
conditioned, are imperfect and provisional, although they cannot be
said to be false (since "while nature may give us those more complete
and convenient, it will not give the lie to those we have already");
while so far as they rest upon what is causal and conditioning, they
are true, general, and necessary. In thus insisting that classification
should be genetic, Leibniz anticipated the great service which the
theory of evolution has done for biological science in enabling science
to form classes which are "natural;" that is, based on identity of
origin.
Leibniz culminates his discussion of classification as a method of
translating the empirical into the rational, by pointing out that
it rests upon the law of continuity; and that this law contains two
factors,--one equivalent to the axiom of the Realists, that nature
is nowhere empty; the other, to that of the Nominalists, that nature
does nothing uselessly. "One of these principles seems to make nature
a prodigal, the other a miser; and yet both are true if properly
understood," says Leibniz. "Nature is like a good manager, sparing
where it is necessary, in order to be magnificent. It is magnificent
in its effects, and economical in the causes used to produce them." In
other words, classification becomes science when it presents us with
both unity and difference. The principle of unity is that of nature
as a miser and economical; that of differentiation is the principle of
nature as prodigal and magnificent. The thoroughly differentiated unity
is nature as self-specifying, or as an organic, not an abstract, unity.
The gist of the whole matter is, then, that experience presents us
with an infinity of ideas, which may appear at first sight arbitrary
and accidental in their connections. This appearance, however, is
not the fact. These ideas are the effects of certain causes; and in
ascertaining these conditions, we reduce the apparently unrelated
variety of experiences to underlying unities, and these unities,
like all real unities or simple beings, are spiritual and rational in
nature. Leibniz's ordinary way of stating this is that the principle
of truths of fact is that of _sufficient reason_. This principle
Leibniz always treats as distinguished from that of identity (and
contradiction) as the ruling category of truths of reason. And we shall
follow him in discussing the two together.
"Our reasonings are based on two leading principles,--that of
contradiction, in virtue of which we judge false all which contains
contradiction, and true that which is opposed or contradictory to that
which is false; and that of sufficient reason, in virtue of which we
judge that no fact is true or actual, no proposition veritable, unless
there is a sufficient reason why it is as it is, and not otherwise,
although these reasons are generally unknown to us. Thus there are
two sorts of truths,--those of reason, and those of fact. The truths
of reason are necessary, and their opposites impossible; while those
of fact are contingent, and their opposites possible. When a truth
is necessary, its reason can be discovered by analysis, resolving
it into ideas and truths that are simpler, until the primitive
truths are arrived at. It is thus that the mathematicians proceed in
reducing by analysis the theorems of speculation and the canons of
practice into definitions, axioms, and postulates. Thus they come to
simple ideas whose definition cannot be given; primitive truths that
cannot be proved, and which do not need it, since they are identical
propositions, whose opposite contains a manifest contradiction."
"But in contingent truths--those of fact--the sufficient reason must
be found; namely, in the succession of things which fill the created
universe,--for otherwise the analysis into particular reasons would
go into detail without limit, by reason of the immense variety of
natural things, and of the infinite divisibility of bodies. There
are an infinity of figures and of past and present movements which
enter into the efficient cause of my present writing, and there are
an infinity of minute inclinations and dispositions of my soul which
enter into its final cause. And since all this detail contains only
other contingent and particular antecedents, each of which has need
of a similar analysis to account for it, we really make no progress by
this analysis; and it is necessary that the final or sufficient reason
be outside the endless succession or series of contingent particulars,
that it consist in a necessary being, in which this series of changes
is contained only _eminenter_, as in its source. This necessary being
and source is what we call God."
In other words, the tracing of empirical facts to their causes and
conditions does not, after all, render them wholly rational. The series
of causes is endless. Every condition is in turn conditioned. We
are not so much solving the problem of the reason of a given fact,
as we are stating the problem in other terms as we go on in this
series. Every solution offers itself again as a problem, and this
endlessly. If these truths of fact, then, are to be rendered wholly
rational, it must be in something which lies outside of the series
considered as a series; that is, something which is not an antecedent
of any one of the series, but is equally related to each and to
all as their ground and source. This, considered as an argument
for the existence of God, we shall deal with hereafter; now we are
concerned only with its bearing upon the relation of experience to
the universality and necessity of knowledge. According to this, the
ultimate meaning of facts is found in their relation to the divine
intelligence; for Leibniz is emphatic in insisting that the relation
of God to experience is not one of bare will to creatures produced by
this will (as Descartes had supposed), but of a will governed wholly
by Intelligence. As Leibniz states it in another connection, not only
matters of fact, but mathematical truths, have the same final basis in
the divine understanding.
"Such truths, strictly speaking, are only conditional, and say that
in case their subject existed they would be found such and such. But
if it is again asked in what consists this conditional connection
in which there is necessary reality, the reply is that it is in
the relation of ideas. And by the further question, Where would
be the ideas if no spirit existed; and what would then become of
the foundation of the certainty of such truths?--we are brought to
the final foundation of truths; namely, that supreme and universal
spirit, which must exist, and whose understanding is, in reality, the
region of the eternal truths. And in order that it may not be thought
that it is not necessary to have recourse to this region, we must
consider that these necessary truths contain the determining reason and
regulative principle of existence, and, in a word, of the laws of the
universe. Thus these necessary truths, being anterior to the existences
of contingent beings, must in turn be based upon the existence of a
necessary substance."
It is because facts are not _mere_ facts, in short, but are the
manifestation of a "determining reason and regulative principle" which
finds its home in universal intelligence, that knowledge of them can
become necessary and general.
The general nature of truths of reason and of their ruling principle,
identity and contradiction, has already been given in the quotation
regarding the principle of sufficient reason. It is Leibniz's
contention that only in truths whose opposite is seen to involve
self-contradiction can we have absolute certainty, and that it is
through connection with such eternal truths that the certainty of
our other knowledge rests. It is thus evident why Leibniz insists, as
against Locke, upon the great importance of axioms and maxims. They are
important, not merely in themselves, but as the sole and indispensable
bases of scientific truth regarding all matters. Leibniz at times,
it is true, speaks as if demonstrative and contingent truths were
of themselves, in principle, distinct, and even opposed. But he also
corrects himself by showing that contingency is rather a subjective
limitation than an objective quality. We, indeed, do not see that the
truth "I exist," for example, is necessary, because we cannot see how
its opposite involves contradiction. But "God sees how the two terms
'I' and 'exist' are connected; that is, _why_ I exist." So far as we
can see facts, then, from the standpoint of the divine intelligence,
so far, it would appear, our knowledge is necessary.
Since these axioms, maxims, or first truths are "innate," we are
in a condition to complete (for the first time) the discussion
of innate ideas. These ideas constitute, as we have learned, the
essential content of the divine intelligence, and of ours so far
as we have realized our identity with God's understanding. The
highest form of knowledge, therefore, is self-consciousness. This
bears the same relation to necessary truths that the latter bear to
experience. "Knowledge of necessary and eternal truths," says Leibniz,
"distinguishes us from simple animals, and makes us have reason and
science, _elevating us to the knowledge of ourselves_. We are thus
developed to self-consciousness; and in being conscious of ourselves we
are conscious of being, of substance, of the simple, of the spiritual,
of God." And again he says that "those that know necessary truths are
rational spirits, capable of self-consciousness, of recognizing what is
termed Ego, substance, and monad. _Thus_ they are rendered capable of
demonstrative knowledge." "We are innate to ourselves; and since we are
beings, being is innate to us, for knowledge of it is implicit in that
which we have of ourselves."
Knowledge, in fine, may be regarded as an ascending series of four
terms. The first is constituted by sensations associated together
in such a way that a relation of antecedence and consequence exists
between them. This is "experience." The second stage comes into
existence when we connect these experiences, not by mere relations of
"consecution," but by their conditions, by the principle of causality,
and especially by that of sufficient reason, which connects them with
the supreme intelligence, God. This stage is science. The third is
knowledge of the axioms and necessary truths in and of themselves,
not merely as involved in science. The fourth is self-consciousness,
the knowledge of intelligence, in its intimate and universal nature,
by which we know God, the mind, and all real substance. In the order of
time the stage of experience is first, and that of self-consciousness
last. But in the lowest stage there are involved the others. The
progress of knowledge consists in the development or unfolding of
this implicit content, till intelligence, spirit, activity, is clearly
revealed as the source and condition of all.